Why is spacetime shown on a 2 dimensional plane?

[Crazyhorse2882]

I don't have the mathematics down quite yet but one thing I've noticed whenever I watch documentaries about gravity in relativity is that it's always described on a 2 dimensional plane. They show a planet bending space time as if the space time is underneath it but I'm thinking that the space time actually encircles the mass creating almost a bubble of sorts around it. Can someone explain this in laymen's terms to me please? Thank you

 

[phinds]

You are correct. This pop-sci analogy is very poor, really, but it DOES give the basic idea of "bending space-time" to the layman. It just isn't accurate at all in any real sense.

Such analogies are often rather poor once you actually understand what is being explained, they just serve as an introduction for laymen.

 

[Drakkith]

How's this picture?

http://orbismediologicus.files.wordpress.com/2009/12/spacetimelu31.jpg

It's a little more accurate than your standard 2d grid.

 

[Chalnoth]

I don't have the mathematics down quite yet but one thing I've noticed whenever I watch documentaries about gravity in relativity is that it's always described on a 2 dimensional plane. They show a planet bending space time as if the space time is underneath it but I'm thinking that the space time actually encircles the mass creating almost a bubble of sorts around it. Can someone explain this in laymen's terms to me please? Thank you

Because it's really, really hard to visualize three-dimensional curvature (let alone four-dimensional space-time curvature). Drakkith's picture isn't bad, but it's still hard to understand what that means (at least to me).

 

[julcab12]

I don't have the mathematics down quite yet but one thing I've noticed whenever I watch documentaries about gravity in relativity is that it's always described on a 2 dimensional plane. They show a planet bending space time as if the space time is underneath it but I'm thinking that the space time actually encircles the mass creating almost a bubble of sorts around it. Can someone explain this in laymen's terms to me please? Thank you

... Here is rough indirect approximation and representation of gravity to a point(). A somewhat similar effect. A few pointers thought. It is important to limit yourself to only what the presentation is trying to convey. 2D appears to give the basic and effective illustration for GR. It is simpler when explained in manifolds. Anyways here is the link.

link: http://www.youtube.com/watch?feature=player_embedded&v=MTY1Kje0yLg

 

[Chalnoth]

... Here is rough indirect approximation and representation of an actual dynamic physical effect of gravity to a point(). A few pointers thought. It is important to limit yourself to only what the presentation is trying to convey.

link: http://www.youtube.com/watch?feature=player_embedded&v=MTY1Kje0yLg

Cool. Though I think one thing to bear in mind is that setup has quite a lot of friction, so it doesn't produce orbits much at all like real ones. If you could produce the same sort of setup, but with minimal friction, that might change. But I doubt that's possible because anything placed on there will deform the sheet, which uses energy and acts as a source of friction. Gravity doesn't have this issue because you don't lose any energy when you deform space-time (if the deformation causes a reduction in the energy of the object doing the deforming, then that energy is stored in the fabric of space-time and not lost...the energy from deforming the sheet is lost to heat).

 

[Chronos]

A fun thing to do [if you are really bored] with 2D spacetime diagrams is try to represent them in 3D using isometric projection.

 

[Clayjay]

I don't have the mathematics down quite yet but one thing I've noticed whenever I watch documentaries about gravity in relativity is that it's always described on a 2 dimensional plane. They show a planet bending space time as if the space time is underneath it but I'm thinking that the space time actually encircles the mass creating almost a bubble of sorts around it. Can someone explain this in laymen's terms to me please? Thank you

The universe is three-dimensional therefore when gravity is projected onto a two-dimensional analog plane it is for demonstration purposes. Gravity collapses space around the center of gravity in three dimensional space but in a two-dimensional analog plain gravity bends space. Only in flatland does gravity bend space.

 

[TumblingDice]

Gravity collapses space around the center of gravity in three dimensional space...

That description sounds like the picture Drakkith linked to in post #3, and as he said, " It's a little more accurate than your standard 2d grid."

Yours is the first mention of 'space' in the thread, as opposed to space-time. I don't think gravity collapses space, but it does create different world lines in space-time - geodesics for mass in inertial frames.

I'm posting outside of my limits here, and standing by to learn more from the experts.

 

[Chalnoth]

Yours is the first mention of 'space' in the thread, as opposed to space-time. I don't think gravity collapses space, but it does create different world lines in space-time - geodesics for mass in inertial frames.

Gravity certainly is a warping of space as well as space-time.

 

[Chronos]

I have no experience in 4D isometric projection. I think I need bigger paper.

 

[Android Neox]

The rubber sheet model is imperfect but still excellent. It shows the curvature of space due to stretching (dilation) in a gravity well. Instead of viewing it from the side, it should be viewed from above because gravitational space dilation is radial... away from the observer. Also, as the sheet is stretched away from the observer, there need to be more lines added, like altitude lines on a topological map. If the lines on the sheet are separated by identical differences in gravitational potential energy, you can relate the difference in time flow between two points as a direct function of how many lines you have to cross to get from one point to the other.

 

[Nugatory]

Instead of viewing it from the side, it should be viewed from above because gravitational space dilation is radial... away from the observer.

If everyone understood and presented the rubber sheet model the way you do, we wouldn't have a problem with it. Unfortunately, very few do, so practically speaking it is a source of misconception and confusion, and that makes it a problem.

The correct picture that you describe is found in many decent textbooks because it's one of the better ways of explaining how a surface with Schwarzschild coordinate $r$ is a sphere of surface area $4\pi{r}^2$ and a surface with Schwarzschild coordinate $r+\Delta{r}$ is a sphere of surface area $4\pi{(r+\Delta{r})}^2$, yet the distance between them is greater than $\Delta{r}$. We just make an analogy between the circumference of circles in the "funnel" and the area of the spheres, and we're there. However, these correct presentations are seldom if ever done in terms of the rubber sheet model, and I will bet long odd against anyone who presents the rubber sheet model as an explanation understanding what's really going on.

 

[Blake Barr]

The key is that if you showed a representation of space-time distortion around a body by drawing the three-dimensional spatial representation you get a drawing that is very confusing and hard to understand. Lines and grids all over the place. A bowling ball on a sheet just works better.

 

[FredKnowsNothing]

Can the explanation of Earth orbiting the sun but not being pulled in because it is moving perpendicular to the curvature of the sun be visualized like a swimmer that can overcome and undertow if they swim perpendicular to the force of the undertow? Also if anyone can explain the way time slows or speeds up relative to gravity or speed i would love to know. For some reason i can't picture how this is possible. From the moment twins are born they would age the same regardless how could one possible age slower based on gravity or speed. How do either of those variables really affect it?

 

[phinds]

Can the explanation of Earth orbiting the sun but not being pulled in because it is moving perpendicular to the curvature of the sun be visualized like a swimmer that can overcome and undertow if they swim perpendicular to the force of the undertow?

I don't get what you are asking but it doesn't matter since the celestial orbits are well understood and there's no need for that kind of analogy (if that is in fact what you're striving for).

Also if anyone can explain the way time slows or speeds up relative to gravity or speed i would love to know. For some reason i can't picture how this is possible. From the moment twins are born they would age the same regardless how could one possible age slower based on gravity or speed. How do either of those variables really affect it?

You should read up on it. Google "The Twin Paradox" and really study it. The different paths through spacetime will likely become clear to you after a while.

Also, just FYI, it is bad form here on PF to hijack a thread in this way. If you have a separate question, start your own thread.

 

[FredKnowsNothing]

I don't get what you are asking but it doesn't matter since the celestial orbits are well understood and there's no need for that kind of analogy (if that is in fact what you're striving for).

You should read up on it. Google "The Twin Paradox" and really study it. The different paths through spacetime will likely become clear to you after a while.

Also, just FYI, it is bad form here on PF to hijack a thread in this way. If you have a separate question, start your own thread.

I agree on the orbit being well understood I was thinking of a way to visualize the forces at play, why the Earth would not crash into the sun, how to think of the feeling on our bodies like the pulling force on your body when in an undertow but how you can overcome that force like the Earth does by moving perpendicular. But let's forget that one.

I get the twin paradox and its fine if calendars and clocks move slower, but biologically regardless of the movement of a second hand the twins bodies would have to be the same, not one older than the other. Or does speed and gravity change our biology in some fashion.

 

[phinds]

I get the twin paradox and its fine if calendars and clocks move slower, but biologically regardless of the movement of a second hand the twins bodies would have to be the same, not one older than the other. Or does speed and gravity change our biology in some fashion.

AGAIN, read about and actually study the Twin Paradox. The different paths through space-time fully explain that the twins CANNOT have the same age when they meet back up. It has nothing to do with biological processes slowing down (they don't) it is just what happens because of different paths through spacetime.

And by the way, clocks and calendars do NOT move slower. In their own frame of reference time passes at one second per second just as it does for the stay at home twin. It's just that different paths through space-time take different numbers of seconds.

 

[Drakkith]

Can the explanation of Earth orbiting the sun but not being pulled in because it is moving perpendicular to the curvature of the sun be visualized like a swimmer that can overcome and undertow if they swim perpendicular to the force of the undertow?

I suppose so, assuming:

1. The water is flowing into something like a large hole from all directions such that the swimmer is moving in an ellipse around the hole.
2. The swimmer is moving quickly enough and never exerts a force towards or away from the hole.

It's certainly not the analogy I would go with though.

Also if anyone can explain the way time slows or speeds up relative to gravity or speed i would love to know.

There are plenty of threads in the Relativity forum dealing with time dilation and the twin paradox. Please have a look there instead of asking in this thread.

 

[phinds]

There are plenty of threads in the Relativity forum dealing with time dilation and the twin paradox ...

You are a master of understatement. At last count there were 18,397

 

[rootone]

... if calendars and clocks move slower, but biologically regardless of the movement of a second hand the twins bodies would have to be the same, not one older than the other. Or does speed and gravity change our biology in some fashion.

Biology and every other chemistry is all subject to the same clock regardless of speed and gravity.
In your own frame of reference one second always passes in one second.
While relative speed or gravity might make it look different to an observer in a different frame,
life for you, and biology in general is unchanged.

 

[phinds]

Biology and every other chemistry is all subject to the same clock regardless of speed and gravity.
In your own frame of reference one second always passes in one second.
While relative speed or gravity might make it look different to an observer in a different frame,
life for you, and biology in general is unchanged.

All true but still does not resolve his confusion because he does not understand different space-time paths creating differing amounts of time passage.

 

[MikeGF]

I don't have the mathematics down quite yet but one thing I've noticed whenever I watch documentaries about gravity in relativity is that it's always described on a 2 dimensional plane. They show a planet bending space time as if the space time is underneath it but I'm thinking that the space time actually encircles the mass creating almost a bubble of sorts around it. Can someone explain this in laymen's terms to me please? Thank you

I have the same issue getting past this “ball on water” depiction of space-time (ST). I would like to see and hear ST depicted as a neutrally buoyant ball (mass) suspended in instead of on water. In that case, and assuming the ball is a perfect sphere and its mass is uniformly distributed, it would displace the same amount of water (ST) at any point around the sphere. How then would the path of that passing mass be effected in terms of bending of ST? I get stuck here, as it seems to me that, in that case, gravity must be an unseen force - a force inconsistent with the two dimensional depictions of bending ST.
I don't have the math. I need to get past this barrier in my thinking.

 

[Drakkith]

I have the same issue getting past this “ball on water” depiction of space-time (ST).

Hmmm. I'm not familiar with this depiction and I can't quite picture it from your description. What do you mean by "it would diplace the same amount of water (ST) at any point around the sphere"?

 

[PeroK]

I don't have the math. I need to get past this barrier in my thinking.

Not having the math is the barrier. As Roger Bacon said nearly 800 years ago:

Mathematics reveals every genuine truth, for it knows every hidden secret and bears the key to every subtlety. Whoever then has the effrontery to study physics while neglecting mathematics should know from the start that he will never make his entry through the portals of wisdom.

 

[PeterDonis]

I would like to see and hear ST depicted as a neutrally buoyant ball (mass) suspended in instead of on water.

Why would you like this? Why do you think it has any relevance to the actual theory of GR?

(Hint: it doesn't.)

 

[PeterDonis]

I need to get past this barrier in my thinking.

The best way to get past this kind of barrier is to give up the idea that you can come up with any useful visualization or intuitive picture without knowing the math and without having tried to work any problems yourself using the theory. Pop science books, articles, and videos try to peddle the fiction that this can be done, but unfortunately it can't. GR simply does not work like anything in your current intuitions; if you want to understand it intuitively, you need to retrain your intuitions. And that requires going through the laborious process of learning the actual theory, which means learning the math.

 

[sophiecentaur]

A fun thing to do [if you are really bored] with 2D spacetime diagrams is try to represent them in 3D using isometric projection.

True but. It’s a bit like trying to make sense / feeling about any partial differential equation is telling you. You look at the x’s and the y’s and the z’s and, if you’re lucky, you can appreciate the higher ‘slopes’ involved. Try to draw the surface and you may ‘get it’ yourself but will you get it across to another person? 2D is a common language and that may be your limit for some models. For orbits , 3D on 2D can help but the risk is that the drum skin will be taken literally and a rubber sheet will fail.
Be prepared for HARD MATHS.

 

[Vanadium 50]

As Roger Bacon said nearly 800 years ago:

About the time this thread was started....